Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2022
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2204.02689 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917935356837888 |
|---|---|
| author | Bera, Sudip |
| author_facet | Bera, Sudip |
| contents | We look for a non-zero $(0, 1)$-vector in the row space of the adjacency matrix $A(Γ)$ of a graph $Γ,$ provided $Γ$ has at least one edge. Akbari, Cameron, and Khosrovshahi conjectured that there exists a non-zero $(0,1)$-vector in the row space of $A(Γ)$ (over the real numbers) which does not occur as a row of $A(Γ).$ This conjecture can be easily verified for graphs having diameter is equal to $1$ (complete graphs). In this article, we affirmatively prove this conjecture for any graph whose diameter is $\geq 4.$ Furthermore, in the remaining two cases that is, for graphs with diameter is equal to $2$ or $3,$ we report some progress in support of the conjecture. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02689 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence of a Non-Zero $(0,1)$-Vector in the Row Space of Adjacency Matrices of Simple Graphs Bera, Sudip Combinatorics 15A03, 05C50 We look for a non-zero $(0, 1)$-vector in the row space of the adjacency matrix $A(Γ)$ of a graph $Γ,$ provided $Γ$ has at least one edge. Akbari, Cameron, and Khosrovshahi conjectured that there exists a non-zero $(0,1)$-vector in the row space of $A(Γ)$ (over the real numbers) which does not occur as a row of $A(Γ).$ This conjecture can be easily verified for graphs having diameter is equal to $1$ (complete graphs). In this article, we affirmatively prove this conjecture for any graph whose diameter is $\geq 4.$ Furthermore, in the remaining two cases that is, for graphs with diameter is equal to $2$ or $3,$ we report some progress in support of the conjecture. |
| title | Existence of a Non-Zero $(0,1)$-Vector in the Row Space of Adjacency Matrices of Simple Graphs |
| topic | Combinatorics 15A03, 05C50 |
| url | https://arxiv.org/abs/2204.02689 |